energies
Article
Impeller Optimized Design of the Centrifugal Pump:
A Numerical and Experimental Investigation
Xiangdong Han 1,2,3 , Yong Kang 1,2,3,4, *, Deng Li 1,2,3 and Weiguo Zhao 5
1
2
3
4
5
*
Key Laboratory of Hydraulic Machinery Transients, Ministry of Education, Wuhan University,
Wuhan 430072, China; hanxiangdong@whu.edu.cn (X.H.); 2008lee@whu.edu.cn (D.L.)
Hubei Key Laboratory of Waterjet Theory and New Technology, Wuhan University, Wuhan 430072, China
School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China
Collaborative Innovation Center of Geospatial Technology, Wuhan 430079, China
School of Energy and Power Engineering, Lanzhou University of Technology, Lanzhou 730050, China;
hanromeolut@163.com
Correspondence: kangyong@whu.edu.cn; Tel.: +86-27-6877-4442
Received: 22 March 2018; Accepted: 17 May 2018; Published: 4 June 2018
Abstract: Combined numerical simulation with experiment, blade wrap angle, and blade exit angle
are varied to investigate the optimized design of the impeller of centrifugal pump. Blade wrap angles
are 122◦ , 126◦ , and 130◦ . Blade exit angles are 24◦ , 26◦ , and 28◦ . Based on numerical simulation,
internal flow of the centrifugal pump with five different impellers under 0.6, 0.8, 1.0, 1.2, and 1.5
Qd are simulated. Variations of static pressure, relative velocity, streamline, and turbulent kinetic
energy are analyzed. The impeller with blade wrap angle 126◦ and blade exit angle 24◦ are optimal.
Distribution of static pressure is the most uniform and relative velocity sudden changes do not exist.
Streamlines are the smoothest. Distribution scope of turbulent kinetic energy is the smallest. Based on
performance experiments, head and efficiency of the centrifugal pump with the best impeller are
tested. The values of head and efficiency are higher than that of the original pump. Centrifugal pump
with the best impeller has better hydraulic performance than the original centrifugal pump.
Keywords: centrifugal pump; impeller; blade wrap angle; blade exit angle; optimized design
1. Introduction
A centrifugal pump is one kind of general machinery [1] which is widely and fully utilized in
the industrial and agricultural fields [2], such as irrigation and water supply. It normally includes
four different parts: suction pipe, impeller, volute, and exit pipe. The impeller is the core part and
it converts the mechanical energy into pressure energy [3], which directly determines the transport
capacity and the hydraulic performances of centrifugal pump. So, optimized design of the impeller is
essential and significant for the efficient operation of a centrifugal pump [4,5].
One-dimensional flow theory, two-dimensional flow theory, and three-dimensional flow theory
are three basic theories to optimally design the centrifugal pump [6,7]. Two-dimensional flow theory
regards the distribution of meridian velocity across the cross-section as symmetrical. The flow is
one kind of potential flow. Optimized design of hydraulic machinery in engineering fields, which
is based on two-dimensional flow theory, is rare. It is only employed to optimally design the higher
specific speed impellers of mixed-flow pump and runners of mixed-flow turbine. Three-dimensional
flow theory, proposed by Wu [8], is also called S1 and S2 relative flow surface theory. In this method,
the three-dimensional flow is converted into two two-dimensional flows in the surfaces S1 and S2 .
Only in the ideal conditions of flow being inviscid, incompressible, and unsteady, can this method be
applied to design the impeller successfully. This method is difficult and complex. Thus, it is not always
Energies 2018, 11, 1444; doi:10.3390/en11061444
www.mdpi.com/journal/energies
Energies 2018, 11, x FOR PEER REVIEW
Energies 2018, 11, 1444
2 of 20
2 of 21
pump in the engineering field. However, one-dimensional flow theory, which is based on Euler
equations,
is optimally
convenient
and an
simple.
Flow
the meridional
is symmetrical.
employed to
design
impeller
forin
a centrifugal
pumpsurface
in the engineering
field. Engineers
However,
coming
from home
and
abroad
factories
widely
employ
one-dimensional
flow
optimally
one-dimensional
flow
theory,
which
is based
on Euler
equations,
is convenient
andtheory
simple.toFlow
in the
design
an impeller
forsymmetrical.
a centrifugalEngineers
pump [9–11].
meridional
surface is
coming from home and abroad factories widely employ
Blade exit angle
andtoblade
wrapdesign
angle (β
are two for
significant
parameters
in the impeller
one-dimensional
flow(Ф)
theory
optimally
an2)impeller
a centrifugal
pump [9–11].
optimized
design
process
to angle
one-dimensional
flow theory
[12–15]. in
The
Blade exit
angle
(Φ) andaccording
blade wrap
(β2 ) are two significant
parameters
thehydraulic
impeller
performance
of a centrifugal
pump isto mainly
determinedflow
by these
In the
actual
optimized design
process according
one-dimensional
theoryparameters.
[12–15]. The
hydraulic
optimized design
process, blade
angle often
varies from
15° parameters.
to 40° and blade
often
performance
of a centrifugal
pumpexit
is mainly
determined
by these
In thewrap
actualangle
optimized
◦
◦
varies
from
90°
to
130°
[16].
Some
scholars
studied
the
effects
of
blade
exit
angle
and
blade
wrap
design process, blade exit angle often varies from 15 to 40 and blade wrap angle often varies from
◦ [16].
angle
hydraulic
performances
of the
the effects
centrifugal
pump
Theblade
selection
bladeon
wrap
90◦ to on
130the
Some scholars
studied
of blade
exit[17–19].
angle and
wrapofangle
the
angle
andperformances
blade exit angle
mainly
depend
on the
specific
of the
centrifugal
pumpand
and
the
hydraulic
of the
centrifugal
pump
[17–19].
Thespeed
selection
of blade
wrap angle
blade
actual
optimized
design on
experience.
If speed
the blade
wrap
angle ispump
too large,
the
impeller
friction
area
exit angle
mainly depend
the specific
of the
centrifugal
and the
actual
optimized
design
becomes
large,
which
bad for
theisimprovement
efficiency.
If the
blade
wrap large,
angle which
is too small,
experience.
If the
bladeiswrap
angle
too large, the of
impeller
friction
area
becomes
is bad
the
impeller
cannot control
the flow
of water
effectively
thesmall,
impeller
cannot operate
stably. For
for the
improvement
of efficiency.
If the
blade wrap
angleand
is too
the impeller
cannot control
the
the
exit effectively
angle, a moderate
value could
effectively
thethe
hydraulic
performances
of the
flowblade
of water
and the impeller
cannot
operateimprove
stably. For
blade exit
angle, a moderate
centrifugal
Comprehensively
considering
the specific
speed
of the pump.
target centrifugal
pump
value
could pump.
effectively
improve the hydraulic
performances
of the
centrifugal
Comprehensively
(n
s = 112) and
thespecific
effectsspeed
of blade
wrap
angle
and bladepump
exit angle
hydraulic
performances
of
considering
the
of the
target
centrifugal
(ns = on
112)the
and
the effects
of blade wrap
the
centrifugal
the variation
scope of
the blade wrap
angle
and blade
exit angle
was selected
angle
and bladepump,
exit angle
on the hydraulic
performances
of the
centrifugal
pump,
the variation
scope
carefully.
The
blade
wrap
angle
was
tested
the selected
range ofcarefully.
120° to 130°
thewrap
values
werewas
Ф =tested
122°,
of the blade
wrap
angle
and
blade
exit
angleinwas
Theand
blade
angle
◦
◦
◦
◦
◦
126°,
and
130°,
respectively.
The
blade
exit
angle
was
tested
in
the
range
of
20°
to
30°
and
the
values
in the range of 120 to 130 and the values were Φ = 122 , 126 , and 130 , respectively. The blade exit
were
2 = 24°,
26°,inand
separately.
angle βwas
tested
the28°,
range
of 20◦ to 30◦ and the values were β2 = 24◦ , 26◦ , and 28◦ , separately.
2. Basic Parameters of the Impeller
The inlet diameter of the impeller
impeller D
D11 = 200 mm and the outlet diameter
diameter D
D22 = 420 mm. The exit
◦ . The original blade exit angle β = 26◦ .
width b22 ==34
34mm.
mm.The
Theoriginal
originalblade
bladewrap
wrap
angle
= 120The
angle
ΦΦ
= 120°.
original blade exit angle β2 = 26°.
2 The
The
parameters
of impeller
the impeller
are shown
in Figure
basicbasic
parameters
of the
are shown
in Figure
1. 1.
Figure
Figure 1.
1. Two-dimensional
Two-dimensional model
model of
of the
the impeller.
impeller.
3. Method to Modify the Impeller
3. Method to Modify the Impeller
The impeller shape is directly determined by the blade profiles. In the impeller optimization
The impeller shape is directly determined by the blade profiles. In the impeller optimization
design process, all blade profiles must be smooth. The bend of the blade profiles should be in one
design process, all blade profiles must be smooth. The bend of the blade profiles should be in one
single direction. An ‘S’ shape should not exist [16,20,21]. All blade profiles should be symmetrical.
single direction. An ‘S’ shape should not exist [16,20,21]. All blade profiles should be symmetrical.
The blade profile differential equation is
The blade profile differential equation is
ds
dθ = ds
dθ = r tan β
r tan β
(1)
(1)
Energies 2018, 11, x FOR PEER REVIEW
3 of 20
Here, s is the axial streamline. θ denotes the axial angle. r represents the radius of one arbitrary
point in the blade profile. β is the blade angle.
Energies
2018,
11, 1444
3 of 21
The
speed
triangle is shown in Figure 2. Here, c represents absolute velocity, w is the relative
velocity, and u is the following velocity. cm and wm are the component of absolute velocity and
relative
velocity
thestreamline.
meridionalθplane,
respectively.
cu is rthe
component
in the of
circumferential
Here,
s is thein
axial
denotes
the axial angle.
represents
the radius
one arbitrary
plane.
point in the blade profile. β is the blade angle.
Based
on the
speed is
triangle,
could2.beHere,
described
as
The
speed
triangle
shown tanβ
in Figure
c represents
absolute velocity, w is the relative
velocity, and u is the following velocity. cm and wm are cthe component of absolute velocity and relative
m
tan
velocity in the meridional plane, respectively.
cuβis=the
component
in the circumferential plane. (2)
u − cu
Based on the speed triangle, tanβ could be described as
Thus,
cm
tan β =
(2)
u
−
cmcu
ds
=
(3)
rdθ u − cu
Thus,
cm
ds
=
(3)
So,
rdθ
u − cu
So,
ds ==
ds
ccm
rdθ
rdθ
u−
u
− ccuu
(4)
(4)
According to the above equations, blade profile optimized design has a closed relation with blade
According to the above equations, blade profile optimized design has a closed relation with
inlet angle (β1 ), blade exit angle (β2 ), and blade wrap angle (Φ). Three different methods are usually
blade inlet angle (β1), blade exit angle (β2), and blade wrap angle (Φ). Three different methods are
employed to modify the blade profiles. They are that
usually employed to modify the blade profiles. They are that
(1)
theconstant.
constant.ββ2 2and
andΦΦare
arechanged.
changed.
(1) ββ11isisthe
(2)
andββ2 2are
arefixed.
fixed.ΦΦisisvaried.
varied.
(2) ββ11and
(3)
β
and
Φ
are
invariant.
β
altered.
(3) β22and Φ are invariant. β1 1isisaltered.
Figure 2.
2. Speed
Speed triangle.
triangle.
Figure
Method 1 (β1 is the constant. β2 and Φ are changed.) was always employed to optimally design
Method 1 (β is the constant. β and Φ are changed.) was always employed to optimally design
the impeller. As 1shown in Table 1, 2the blade exit angle of Schemes 1–3 was identical and the blade
the impeller. As shown in Table 1, the blade exit angle of Schemes 1–3 was identical and the blade
wrap angles varied from 122° to 130°, which were employed to investigate the effects of different
wrap angles varied from 122◦ to 130◦ , which were employed to investigate the effects of different blade
blade wrap angles on the optimized design of the centrifugal pump. For Schemes 2, 4, and 5, the
wrap angles on the optimized design of the centrifugal pump. For Schemes 2, 4, and 5, the blade wrap
blade wrap angle was the same and the blade exit angle was changed, which was used to discuss the
angle was the same and the blade exit angle was changed, which was used to discuss the effects of
effects of diverse blade exit angles on the optimized design of the centrifugal pump.
diverse blade exit angles on the optimized design of the centrifugal pump.
Table 1. Optimized schemes of the blade profile.
Table 1. Optimized schemes of the blade profile.
Scheme
1
2
3
4
5
130°
126° 4 126° 5
Scheme Φ 1 122° 126°
2
3
◦
β2 122◦ 26° 126
26°
26°
Φ
130◦ 28°126◦24° 126◦
β2
26◦
26◦
26◦
28◦
24◦
The impeller optimized design procedure is that, via the analysis of effects of blade wrap angle
(Schemes 1–3) on the hydraulic performances of the centrifugal pump, one optimal scheme could be
The impeller
optimized design
is that, According
via the analysis
effects of blade
wrap
determined
via computational
fluid procedure
dynamics (CFD).
to theofdiscussion
of effects
of angle
blade
(Schemes 1–3) on the hydraulic performances of the centrifugal pump, one optimal scheme could be
determined via computational fluid dynamics (CFD). According to the discussion of effects of blade
exit angle (Schemes 2, 4, and 5) on the variations of head and efficiency, one optimal scheme could be
Energies 2018, 11, x FOR PEER REVIEW
Energies
2018,
11, 1444
Energies
2018,
11, x FOR PEER REVIEW
4 of 20
4 of 4
20of 21
exit angle (Schemes 2, 4, and 5) on the variations of head and efficiency, one optimal scheme could
exit by
angle
(Schemessimulation.
2, 4, and 5) Then,
on the these
variations
head and
efficiency,
optimal and
scheme
be got
numerical
two of
different
schemes
areone
compared
thecould
best one
got be
by got
numerical
simulation.
Then,Then,
thesethese
two different
schemes
are compared
andand
thethe
bestbest
oneone
could
by
numerical
simulation.
two
different
schemes
are
compared
could be obtained. The optimized procedure includes two main parts, as shown in Figure 3.
be obtained.
The
optimized
procedure
includes
two
main
parts,
as
shown
in
Figure
3.
could be obtained. The optimized procedure includes two main parts, as shown in Figure 3.
Figure 3. Flow chart of the optimized design of the impeller.
Figure
3. Flow chart of the optimized design of the impeller.
Figure 3. Flow chart of the optimized design of the impeller.
The physical models of the blades under different blade wrap angle and blade exit angle
The
models
the
blades
underunder
different
blade wrap
and
bladeand
exit blade
angle conditions
conditions
are given
in of
Figure
4. blades
Thephysical
physical
models
of the
different
bladeangle
wrap
angle
exit angle
are
given inare
Figure
4. in Figure 4.
conditions
given
Impeller 1
(Φ = 122°, β2 = 26°)
Impeller 1
(Φ = 122°, β2 = 26°)
Impeller 2
(Φ = 126°, β2 = 26°)
Impeller 3
(Φ = 130°, β2 = 26°)
Impeller 4
(Φ = 126°, β2 = 28°)
Impeller 2
Impeller 3
Impeller 4
of the(Φ
blades.
(Φ = 126°, β2 = Figure
26°) 4.
(ΦPhysical
= 130°, βmodel
2 = 26°)
= 126°, β2 = 28°)
4. Numerical Method
Impeller 5
(Φ = 126°, β2 = 24°)
Impeller 5
(Φ = 126°, β2 = 24°)
Figure 4. Physical model of the blades.
Figure 4. Physical model of the blades.
4.1. Fundamental
Equations
4. Numerical
Method
4. Numerical Method
The fundamental equations [22] are employed to describe the flow characteristics in the
4.1. Fundamental
Equations
pump,
which include two main parts: continuity equation and motion equation,
4.1. centrifugal
Fundamental
Equations
corresponding
with
conservation
momentum
conservation
The fundamentalmass
equations
[22] law
are and
employed
to describe
the law.
flow characteristics in the
The fundamental equations [22] are employed to describe the flow characteristics in the centrifugal
centrifugal pump, which include two main
parts:
continuity
equation
and motion equation,
( ρui ) = 0 and motion equation,
∂ρ ∂equation
pump, which include two main parts: continuity
corresponding
with
+
(5)
corresponding with mass conservation law and
conservation law.
∂t momentum
∂xi law.
mass conservation law and momentum conservation
∂ ( ρ ui)
∂u
∂u
∂ρ∂∂pρ ∂∂(ρu
) ∂u=i 0+ ∂uj   − 2 ∂  μ ∂uj 
ρ i + ρ uj i = ρ fi − ∂t+++ ∂xμi  =
(6) (5)
0 ∂x  3 ∂x  ∂x 
(5)
∂t
∂x j
i  ∂x
∂t∂xi ∂x∂x
j 
i 
i 
j 
i  j

"   ∂u ∂u  !#2 ∂  ∂u 
!
∂ui of water.
∂u t represents
∂p
∂the
Here, ρ is the density
time. u denotes
the velocity.
j
 μ ∂uii + ∂uj −
∂ui ρ ∂u
2 μ∂ j  ∂uxj is the Cartesian (6)
fi −
+i ρ uj i = ρ ∂p
+∂
 3 −
 ∂x µ
ρ the body
(6)
+ ρu∂jforce
=
t
∂ρxfji −p is the
∂+x pressure.
∂x µ  ∂μxis+
∂xi dynamic
∂xi viscosity.
coordinate. fi is
vector.
the
∂t
∂x j
∂xi i ∂x j j  ∂x jj
∂xi
3 ∂xi j  ∂x j
Here, ρρ isis the
the density
density of
ofwater.
water. tt represents
represents the
the time.
time. uu denotes
denotes the
the velocity.
velocity. xx is
is the
the Cartesian
Cartesian
Here,
coordinate.
f
i is the body force vector. p is the pressure. μ is the dynamic viscosity.
coordinate. f i is the body force vector. p is the pressure. µ is the dynamic viscosity.
Energies 2018, 11, 1444
5 of 21
4.2.
Turbulent
Energies
2018, 11, xModel
FOR PEER REVIEW
5 of 20
RNG k-ε turbulent model proposed by Yakhot and Orzag [23] was employed to deal with turbulent
4.2. Turbulent Model
flow. In the centrifugal pump, the impeller is the rotating part whose rotation effects could be fully
turbulentdissipation
model proposed
Yakhot in
and
[23] was
employed
dealhand,
with the RNG
dealt RNG
by thek-ε
turbulent
rate (ε)by
equation
thisOrzag
turbulent
model.
On theto
other
turbulent flow. In the centrifugal pump, the impeller is the rotating part whose rotation effects could
k-ε turbulent model has high-precision, which could guarantee the accuracy of the numerical results.
be fully dealt by the turbulent dissipation rate (ε) equation in this turbulent model. On the other
" which could guarantee
#
hand, the RNG k-ε turbulent model has high-precision,
the accuracy of the
∂k
∂
∂(ρk) ∂(ρkui )
numerical results.
+
=
× (αk (µ + µt ))
+ Gk + ρε
∂t
∂ (ρk)
∂t
∂xi
+
∂ ( ρ kui )
∂xi
∂x j
=
∂x j
∂ 
∂k 
×  α ( μ + μt )
+ ρε
 + G"
k
x
∂x j  k
∂
ε
ε2 j  ∂
(
)
∂(ρε) ∂(ρεui )
∂ε
+
= C1ε Gk C2ε ρ +
α ε ( µ + µt )
2
∂t
∂x
k
k
∂x
∂x
∂ ( ρε ) ∂ ( ρε ui )i
j
ε
ε
∂  j
∂ε 
∂t
+
∂xi
= C1ε
G k −C 2ε ρ
+
∂x
α ε ( μ +μ t )
∂x
#

(7)
(7)
(8)
(8)

j 
k2 j 
(9)
µt = ρcµ
ε
k2
(9)
μ t =ρ c μ
Here, k is the turbulent kinetic energy. ε isεthe turbulent dissipation rate. µt is the turbulent
viscosity.
The five terms, C , C2ε , αenergy.
c are empirical coefficients and the values are 1.42, 1.68,
k , αε , and
Here, k is the turbulent1εkinetic
ε is µthe turbulent dissipation rate. μt is the turbulent
1.39,
1.39, The
andfive
0.09,
separately.
Gkk, αisε, one
term
of turbulent
kinetic
energy
which
viscosity.
terms,
C1ε, C2ε, α
and generation
cμ are empirical
coefficients
and the
values
are 1.42,
1.68, is caused
by
the
mean
velocity
gradient.
1.39, 1.39, and 0.09, separately. Gk is one generation term of turbulent kinetic energy which is caused
k
k
by the mean velocity gradient.
5. Numerical Simulation Setup
5. Numerical Simulation Setup
5.1. Physical Model
5.1. Physical Model
Three-dimensional (3D) single-stage and single-suction centrifugal pump was employed,
Three-dimensional
(3D)suction
single-stage
and single-suction
centrifugal
pump was
employed,
as pipe was
as shown
in Figure 5. The
pipe was
employed to keep
the uniform
of the
flow. Exit
shown intoFigure
The
suction pipe
employed to
keep the uniform
of the flow.
Exit
pipe
utilized
avoid5.the
backflow.
Thewas
performance
parameters
were designed
flow
rate
Qdwas
= 550 m3 /h;
3
utilized tohead
avoidHthe=backflow.
The motor
performance
wereand
designed
rate Qdspeed
= 550 m
designed
50 m; rated
powerparameters
P = 110 KW;
rated flow
rotational
n /h;
= 1480 rpm.
d
designed head Hd = 50 m; rated motor power P = 110 KW; and rated rotational speed n = 1480rpm.
The geometric parameters of the impeller and the volute were shown in Table 2.
The geometric parameters of the impeller and the volute were shown in Table 2.
Volute
Exit pipe
Suction pipe
Impeller
Figure 5. Physical model of the centrifugal pump.
Figure 5. Physical model of the centrifugal pump.
Table 2. Geometric parameters of the impeller and volute
Table 2. Geometric parameters of the impeller and volute
Parameter
Value
Impeller inlet diameter D1, mm
200
Parameter
Impeller outlet diameter D2, mm
420
Impeller
diameter
D1 , mm 34
b2, mm
Impellerinlet
exit width
Impeller
outletofdiameter
Number
blade Z D2 , mm 6
Impellerof
exit
, mm
435
Base diameter
thewidth
voluteb2D, 3mm
Number
of
Z
b3, mm
72
Volute inlet widthblade
Base
diameter
of the volute
D3 , mm 250
Volute
outlet diameter
D4, mm
Value
200
420
34
6
435
Volute inlet width b3 , mm
72
Volute outlet
diameter
D4 , mm
250 and back chamber
To get accurate numerical simulation
results
a balance
hole, front chamber,
were added to the 3D physical model of the centrifugal pump, as displayed in Figures 6 and 7.
Diameter of the balance hole was 10mm and it was mainly employed to balance the axial force [24].
To get accurate numerical simulation results a balance hole, front chamber, and back chamber were
added to the 3D physical model of the centrifugal pump, as displayed in Figures 6 and 7. Diameter of
the balance hole was 10mm and it was mainly employed to balance the axial force [24].
Energies 2018, 11, x FOR PEER REVIEW
Energies 2018, 11, 1444
6 of 20
6 of 21
Energies 2018, 11, x FOR PEER REVIEW
Energies 2018, 11, x FOR PEER REVIEW
6 of 20
6 of 20
Figure
modelofofthe
theimpeller.
impeller.
Figure6.6.Physical
Physical model
Figure
modelofofthe
theimpeller.
impeller.
Figure6.6.Physical
Physical model
Figure 7. Chamber of the centrifugal pump.
Figure 7. Chamber of the centrifugal pump.
Figure
Figure7.7. Chamber
Chamberof
ofthe
thecentrifugal
centrifugalpump.
pump.
5.2. Mesh Generation
5.2. Mesh Generation
5.2.
Generation
5.2. Mesh
MeshANSYS-ICEM
Generation (15.0, ANSYS, Inc., Canonsburg, PA, USA) is employed to discrete the
ANSYS-ICEM
(15.0, ANSYS,domains.
Inc., Canonsburg,
PA,theUSA)
is employed
to discrete
the
centrifugal
pump computational
To guarantee
uniformity
of the flow,
structured
centrifugal
pump
computational
domains.
To guarantee
the is
uniformity
oftopipe
the
flow,
structured
ANSYS-ICEM
(15.0,
ANSYS,
Inc.,
Canonsburg,
PA,domains
USA)
discrete
thediscrete
centrifugal
ANSYS-ICEM
(15.0,
Inc.,
Canonsburg,
PA,
USA)
is employed
to
meshes
were
employed
toANSYS,
discretize
the
computational
ofemployed
the suction
and exit
pipe,
as the
meshes
were
employed
to Fully
discretize
the computational
domains
the
suction
pipe
andthe
exitvolute,
pipe,
as
pump
computational
domains.
To
guarantee
uniformity
ofuniformity
the
flow,
structured
meshes
centrifugal
pump
computational
domains.
Tothe
guarantee
theof
of and
the
flow,
structured
displayed
in Figure
8d–e.
considering
the
complex
structure
of
the
impeller
towere
displayed
in
Figure
8d–e.
Fully
considering
the
complex
structure
of
the
impeller
and
the
volute,
to
get
the
better
adaptability
of
the
flow,
unstructured
meshes
were
employed
to
discrete
the
employed
to discretize
domains of the
suction of
pipe
exit pipe
pipe,and
as displayed
meshes were
employedthe
to computational
discretize the computational
domains
theand
suction
exit pipe, in
as
get
the better domains
adaptability
of the flow,
unstructured
meshes
employed
toin discrete
the
computational
of impeller,
front and
chamber,
andwere
volute,
shown
Figure
8a–c.
Figure
8d–e.
considering
the
complex
structure
of the
impeller
volute,
to get
better
displayed
inFully
Figure
8d–e. Fully
considering
theback
complex
structure
ofand
theasthe
impeller
and
the the
volute,
to
computational
domains
of impeller,
front and
back
chamber,
and refined.
volute, as shown in Figure 8a–c.
Meshes
in
leading
edges
and
balance
hole
were
adaptability
ofthe
the
flow, unstructured
meshesunstructured
were
employed
to discrete
computational
domains
get the
better
adaptability
ofof the
the impeller
flow,
meshes
were the
employed
to discrete
the
Meshes in the leading edges of the impeller and balance hole were refined.
of
impeller, frontdomains
and backofchamber,
volute,
shown
in Figure
Meshes
in thein
leading
computational
impeller,and
front
and as
back
chamber,
and8a–c.
volute,
as shown
Figureedges
8a–c.
of
the impeller
and balance
were
refined.and balance hole were refined.
Meshes
in the leading
edgeshole
of the
impeller
(a) Mesh of the impeller
(a) Mesh of the impeller
(a) Mesh of the impeller
Figure 8. Cont.
Energies 2018, 11, 1444
7 of 21
Energies 2018, 11, x FOR PEER REVIEW
Energies 2018, 11, x FOR PEER REVIEW
7 of 20
7 of 20
(b) Mesh of the cover plate
(b) Mesh of the cover plate
(c) Mesh of the volute
(c) Mesh of the volute
(e) Mesh of the exit pipe
(d) Mesh of the suction pipe
(e) Mesh of the exit pipe
(d) Mesh of the suction pipe
Figure 8. Meshes of the computational domain of the centrifugal pump.
Figure 8. Meshes of the computational domain of the centrifugal pump.
Figure 8. Meshes of the computational domain of the centrifugal pump.
Mesh numbers of the five different impellers were 3,472,923, 3,473,052, 3,471,896, 3,472,816, and
Mesh
numbersof
ofthe
thefive
fivedifferent
different
impellers
were
3,472,923,
3,473,052,
Mesh respectively.
numbers
were
3,472,923,
3,473,052,
3,471,896,
3,472,816,
3,473,011,
All
mesh
qualityimpellers
was
higher
than
0.3.
Mesh
number
and3,471,896,
quality
of 3,472,816,
front and
and
and
3,473,011,
respectively.
All
mesh
quality
was
higher
than
0.3.
Mesh
number
and
quality
of
front
3,473,011,
respectively.
All
mesh
quality
was
higher
than
0.3.
Mesh
number
and
quality
of
front
and
back chamber, volute, suction pipe, and exit pipe were displayed in Table 3.
and
chamber,
volute,
suction
displayed
in Table
backback
chamber,
volute,
suction
pipe,pipe,
and and
exit exit
pipepipe
werewere
displayed
in Table
3. 3.
Table 3. Mesh number and quality
Table 3. Mesh number and quality
Table
3. Mesh number and quality
Volute
Front and Back Chamber
Back
Chamber
Volute
Frontand
and
Back
Chamber Volute
Mesh number Front
934,607
2,238,179
Mesh
number
934,607
2,238,179
Mesh
number
934,607
2,238,179
Mesh
quality
>0.4
>0.4
Mesh
quality
>0.4
>0.4
Mesh
quality
>0.4
>0.4
Suction Pipe
Suction
Pipe
Suction
Pipe
498,506
498,506
498,506
>0.8
>0.8
Exit Pipe
Exit
Pipe
Exit
Pipe
327,624
327,624
327,624
>0.8
>0.8
>0.8
Head under designed flow rate condition was calculated to verify mesh independence. Results
Head
under
designed
flow rate
condition
was calculated
to verify
mesh independence.
Results
indicated
with
the increase
of mesh
number,
head increased
firstly.
the differences
of
Head that
under
designed
flow rate
condition
was calculated
to verify
meshThen,
independence.
Results
indicated
that
with
the
increase
of mesh
number,
head
increased
firstly.
Then, centrifugal
the differences
of
head
were
slight,
as
shown
in
Figure
9.
Total
mesh
numbers
of
the
five
different
pumps
indicated that with the increase of mesh number, head increased firstly. Then, the differences of head
head
were
slight,
as shown
in Figure7,145,682,
9. Total mesh
numbers separately.
of the five different centrifugal pumps
were slight,
7,139,826,
7,146,497,
7,143,016,
and 7,147,024,
were
as shown
in Figure
9. Total mesh numbers
of the five different centrifugal pumps were
were 7,139,826, 7,146,497, 7,143,016, 7,145,682, and 7,147,024, separately.
7,139,826, 7,146,497, 7,143,016, 7,145,682, and 7,147,024, separately.
Figure 9. Meshes independence.
Figure 9. Meshes independence.
5.3. Boundary Conditions
5.3. Boundary Conditions
Energies 2018, 11, 1444
8 of 21
Energies2018,
2018,11,
11,xxFOR
FORPEER
PEERREVIEW
REVIEW
Energies
88ofof2020
5.3. Boundary Conditions
Reynoldsaveraged
averagedNaiver–Stokes
Naiver–Stokes(RANS)
(RANS)method
methodwas
wasemployed
employedto
tosimulate
simulatethe
theinternal
internalflow
flow
Reynolds
employed
to
simulate
the
internal
flow
thecentrifugal
centrifugalpump.
pump.At
Atinlet,
inlet,the
thevelocity
velocitywas
wasset.
set.At
Atoutlet,
outlet,the
thefree
freeoutflow
outflowwas
wasset.
set.Near
Nearwall
wall
ofofthe
At
outlet,
flowwas
wastreated
treatedby
bystandard
standardwall
wallfunction.
function.The
The
interface
was
set
between
suction
pipe
and
impeller,
flow
interface
was
set
between
suction
pipe
and
impeller,
The interface was set between suction pipe and impeller,
impellerand
and
volute,
volute
and
exit pipe.
pipe.
The SIMPLE
SIMPLE
scheme
was
used to
to solve
solve the
the
coupled
impeller
and
volute,
volute
The
scheme
was
coupled
volute,
volute
andand
exitexit
pipe.
The SIMPLE
scheme
was used
toused
solve
the
coupled
equations
equations
velocity.
ThePRESTO!
PRESTO!
wasemployed
employed
computepressure.
pressure.
Theorder
second
orderupwind
upwind
equations
velocity.
The
was
totocompute
The
second
order
of
velocity.ofofThe
PRESTO!
was
employed
to compute
pressure.
The second
upwind
scheme
scheme
was
used
for
the
solving
of
momentum,
turbulent
kinetic
energy,
and
turbulent
dissipation
scheme
was
used
for
the
solving
of
momentum,
turbulent
kinetic
energy,
and
turbulent
dissipation
was used for the solving of momentum, turbulent kinetic energy, and turbulent dissipation rate.
rate.
Allresiduals
residuals
were
less1.0
than
1.0−××510
rate.
All
less
than
All
residuals
were were
less
than
×1.0
10
.10−5−5. .
Verification
5.4.Verification
Verificationofofthe
theAlgorithm
Algorithm
5.4.
above-mentioned
algorithm
isisemployed
employed
to
numerically
simulate
the
internal
flow
Theabove-mentioned
above-mentionedalgorithm
algorithmis
employedto
tonumerically
numericallysimulate
simulatethe
theinternal
internalflow
flowofofthe
the
The
original
centrifugal
To
verify
the
reasonableness
of
originalcentrifugal
centrifugalpump
pumpand
andoptimized
optimizedcentrifugal
centrifugalpump.
pump.To
Toverify
verifythe
thereasonableness
reasonablenessof
ofthe
the
original
algorithm
used,
flow
in
one
single-stage
and
single
suction
centrifugal
pump
which
isisshown
shown
algorithmused,
used,flow
flowin
inone
onesingle-stage
single-stageand
andsingle
singlesuction
suctioncentrifugal
centrifugalpump
pumpwhich
whichis
showninin
algorithm
33/h
3/h
conditions.
The
rated
flow
rate
isisis
QQ
500
m
Figure10
10was
wassimulated
simulatedunder
underdifferent
differentflow
flowrate
rate
conditions.
The
rated
flow
rate
d==
500
Figure
was
simulated
under
different
flow
rate
conditions.
The
rated
flow
rate
d=
500
mm
/h
dQ
and
53
m.
Ratedrotating
rotating
speed
1480rpm.
rpm.
andthe
therated
ratedhead
headisisHHddd===53
53m.
m.Rated
rotatingspeed
speedisis
isnnn===1480
Figure10.
10.Experimental
Experimentalcentrifugal
centrifugalpump.
pump.
Figure
Figure 10. Experimental centrifugal pump.
Thenumerical
numericalresults
resultsofofhead
headand
andefficiency
efficiency had
hadaagood
goodagreement
agreementwith
withthe
theexperimental
experimental
The
Theas
numerical
results
of head
had
a good
agreement
with
the
experimental
results,
results,
as
displayed
Figure
11.and
Theefficiency
maximum
relative
error
thehead
headwas
was
lessthan
than3.7%.
3.7%.
The
results,
displayed
ininFigure
11.
The
maximum
relative
error
ofofthe
less
The
as
displayed
in
Figure
11.
The
maximum
relative
error
of
the
head
was
less
than
3.7%.
The
largest
largest
fractional
error
of
the
efficiency
was
less
than
2.2%.
The
algorithm
designed
was
reasonable.
largest fractional error of the efficiency was less than 2.2%. The algorithm designed was reasonable.
fractional error of the efficiency was less than 2.2%. The algorithm designed was reasonable.
6060
7878
5555
Efficiency η/%
Efficiency η/%
7575
5050
Head H/m
Head H/m
7272
6969
4545
4040
3535
3030
200
200
6666
Experimentalresults
results
Experimental
Numericalsimulation
simulationresults
results
Numerical
300
300
400
400
500
500
600
600
3 3·h
Flowrate
rateQ/
Q/mm
Flow
·h-1
700
700
Experimentalresults
results
Experimental
Numericalsimulation
simulationresults
results
Numerical
6363
6060
800
800
-1
(a)
(a)
200
200
300
300
400
400
500
500
600
600
3 3·h
Flowrate
rateQ/
Q/mm
Flow
·h-1
700
700
800
800
-1
(b)
(b)
Figure
Comparison
of theof
hydraulic
performances
of centrifugal
(a) Head
(H)-flow
rate
(Q);
Figure11.
11.
Comparison
of
the hydraulic
hydraulic
performances
centrifugal
pump.
(a)
Head
Figure
11.
Comparison
the
performances
ofofpump.
centrifugal
pump.
(a)
Head
(b)
Efficiency
(η)-flow
rate
(Q).
(H)-flow
rate
(Q).
(b)
Efficiency
(η)-flow
rate
(Q).
(H)-flow rate (Q). (b) Efficiency (η)-flow rate (Q).
NumericalSimulation
SimulationResults
ResultsAnalysis
Analysis
Numerical
6.6.Numerical
Tomeasure
measure
the
effects
blade
wrap
angle
andexit
blade
exit
angle
on the
the performances
performances
the
effects
of blade
wrapwrap
angleangle
and
blade
angle
onangle
the
performances
of centrifugal
To
measure
the
effects
ofof blade
and
blade
exit
on
ofof
centrifugal
pump,
variations
static
pressure,
relative
velocity,and
streamlines,
and
turbulent
kinetic
pump,
variations
ofvariations
static pressure,
relative
velocity,
streamlines,
turbulentand
kinetic
energykinetic
in the
centrifugal
pump,
ofofstatic
pressure,
relative
velocity,
streamlines,
turbulent
energyin
inthe
the
middle
spanofwere
ofthe
theanalyzed
impellerwere
wereanalyzed
analyzed
under
thetypical
typical
flow(low
rateconditions
conditions
(low
middle
span
ofmiddle
the impeller
under
the typical
flowthe
rate
conditions
flow
rate 0.6
Qd
energy
span
impeller
under
flow
rate
(low
flow0.8
rate
0.6
and
0.8
rated
flow
rateflow
1.0QQ
and
high
flow
rate
1.2
andvariations
1.5QQd).
d).Also,
Also,
the
and
Qd0.6
, rated
flow0.8
rate
Qd , and
high
rate
1.2 high
Q
1.5rate
Qd ).1.2
Also,
the
of head
flow
rate
QQd dand
QQd1.0
,d,rated
flow
rate
1.0
d,d,and
flow
QQd dand
1.5
the
d and
variations
head
and
efficiency
under
the
aboveflow
flow
rate
conditionswere
werecompared.
compared.
and
efficiency
under
the
above flow
ratethe
conditions
were
compared.
variations
ofofhead
and
efficiency
under
above
rate
conditions
6.1.Variation
VariationofofStatic
StaticPressure
Pressure
6.1.
Energies 2018, 11, 1444
9 of 21
6.1. Variation of Static Pressure
Energies 2018, 11, x FOR PEER REVIEW
9 of 20
The overall static pressure variation law is that static pressure in different passages distributed
The
overall static
variationin
law
that staticwere
pressure
in different
passages
distributed
uniformly.
Differences
ofpressure
static pressure
allispassages
relatively
small,
as shown
in Figure 12.
uniformly. Differences of static pressure in all passages were relatively small, as shown in Figure 12.
At the inlet of the impeller, static pressure was the lowest. Static pressure at the outlet of the impeller
At the inlet of the impeller, static pressure was the lowest. Static pressure at the outlet of the impeller
was the highest. For Impellers 1–5, static pressure increased overall with the growing of flow rate.
was the highest. For Impellers 1–5, static pressure increased overall with the growing of flow rate.
Under
0.8 Q
the
staticpressure
pressure
was
more
manifest.
At outlet,
static pressure
d condition,
Under
0.8
Qd condition,
theincrease
increase of
of static
was
more
manifest.
At outlet,
static pressure
attained
the maximum
under
attained
the maximum
under1.5
1.5QQdd condition.
condition.
0.6 Qd
0.8 Qd
1.0 Qd
1.2 Qd
1.5 Qd
1.2 Qd
1.5 Qd
(a) Impeller 1 (Φ = 122°, β2 = 26°)
0.6 Qd
0.8 Qd
1.0 Qd
(b) Impeller 2 (Φ = 126°, β2 = 26°)
0.6 Qd
0.8 Qd
1.0 Qd
1.2 Qd
1.5 Qd
1.2 Qd
1.5 Qd
(c) Impeller 3 (Φ = 130°, β2 = 26°)
0.6 Qd
0.8 Qd
1.0 Qd
(d) Impeller 4 (Φ = 126°, β2 = 28°)
0.6 Qd
0.8 Qd
1.0 Qd
(e) Impeller 5 (Φ = 126°, β2 = 24°)
Figure 12. Cont.
1.2 Qd
1.5 Qd
Energies 2018, 11, 1444
10 of 21
Energies 2018, 11, x FOR PEER REVIEW
10 of 20
Figure 12. Variation of static pressure in different impellers.
Figure 12. Variation of static pressure in different impellers.
Static pressure in Impellers 1, 2, and 4 fluctuated more obviously and the pressure gradient was
Static
pressure
in Impellers
1, 2,intense
and 4rotor-stator
fluctuatedinteraction
more obviously
and theand
pressure
gradient
higher,
which was
caused by the
of the impeller
the volute
[25]. was
Volumetric
losscaused
of the centrifugal
pumprotor-stator
is severe. Thus,
the centrifugal
could
not
operate
higher,
which was
by the intense
interaction
of the pump
impeller
and
the
volute [25].
efficiently.
2,
under pump
low flow
conditions,
scope
of lower
pressure
Energies loss
2018,For
11,
FOR PEER
REVIEW
10
of operate
20
Volumetric
ofxImpeller
the
centrifugal
is rate
severe.
Thus,the
thedistribution
centrifugal
pump
could
not
was
much
larger
than
that
of
other
impellers.
Centrifugal
pumps
operating
under
these
conditions
efficiently. For Impeller 2, under low flow rate conditions, the distribution scope of lower pressure was
were unstable. Compared with Impellers 1, 2, 4, and 5, the lower pressure region in Impeller 3 was
much larger than that of other impellers. Centrifugal pumps operating under these conditions were
much larger under 0.8 Qd and 1.2 Qd conditions, mainly caused by secondary flow. Cavitation in
unstable.
Compared with Impellers 1, 2, 4, and 5, the lower pressure region in Impeller 3 was much
Impeller 3 could occur easily, which could make the performances of the centrifugal pump decrease
largersharply
under [26].
0.8 QInd Impeller
and 1.2Figure
Qdthe
conditions,
mainly
caused
secondary
flow. pressure
Cavitation
in Impeller
3
5,
pressure
gradient
the smallest
andimpellers.
the lower
region
was
12.
Variation
of staticwas
pressure
inby
different
couldthe
occur
easily,
which
make
the performances
theoptimization
centrifugalof
pump
decrease
smallest
under
all could
flow rate
conditions,
proving thatofthe
Impeller
5 is thesharply
best. [26].
Static
pressure
in Impellers
1,was
2,
and
4 fluctuated
more
obviously
and
thesafety
pressure
gradient
Impeller
Ф = 126°
and blade
exit
angles
β2 = 24°and
could
guarantee
the
operation
of was
the
In Impeller
5, with
the
pressure
gradient
the
smallest
the
lower pressure
region
was the
smallest
higher,
which
was
caused byproving
the intense
rotor-stator
interaction
the impeller
volute
[25]. with
pump.
undercentrifugal
all flow
rate
conditions,
that
the optimization
ofofImpeller
5 is and
the the
best.
Impeller
Volumetric
loss of the centrifugal pump
is severe. Thus, the centrifugal pump could not operate
◦ and blade
Φ = 126
exit angles β2 = 24◦ could
guarantee the safety operation of the centrifugal pump.
6.2.
VariationFor
of Relative
efficiently.
ImpellerVelocity
2, under low flow rate conditions, the distribution scope of lower pressure
was
much
larger
than
that
of other impellers. Centrifugal pumps operating under these conditions
6.2. Variation
of Relative
Velocity
At the
inlet of the
impeller, the relative velocity was small. At the outlet of the impeller, the
were unstable. Compared with Impellers 1, 2, 4, and 5, the lower pressure region in Impeller 3 was
relative velocity attained the maximum, which was in agreement with the experimental and
At
the inlet
the impeller,
the1.2
relative
velocity was
small.
At by
thesecondary
outlet of the
impeller,
thein
relative
much
largerofunder
0.8 Qd and
Qd conditions,
mainly
caused
flow.
Cavitation
theoretical results [27]. Relative velocity in the pressure surface was much smaller than that of
Impeller
3 could
occur
easily, which
could
make
the
performances
ofthe
the experimental
centrifugal pump
decrease
velocity
attained
the
maximum,
which
was
in
agreement
with
and
theoretical
suction pressure. With the increase of flow rate, the low relative speed zone became smaller, as
sharply
[26]. In Impeller
5, in
thethe
pressure
gradient
was was
the smallest
and the lower
region was
resultsshown
[27]. in
Relative
velocity
pressure
surface
much smaller
than pressure
that of suction
pressure.
Figure 13.
the smallest under all flow rate conditions, proving that the optimization of Impeller 5 is the best.
With the increase
of flow
flowrate
rate,
the low relative
speed
zonezone
became
smaller,
as smaller
shownthan
in Figure
Under low
conditions,
low relative
velocity
in Impeller
5 was
that of 13.
Impeller with Ф = 126° and blade exit angles β2 = 24° could guarantee the safety operation of the
other impellers,
could guarantee
the stable
operation
centrifugal
Velocity
Under
low flow which
rate conditions,
low relative
velocity
zoneof
in the
Impeller
5 waspump.
smaller
than that of
centrifugal pump.
in which
Impellers
1–4 guarantee
was larger the
and stable
the flow
in these of
impellers
was disorderly.
rated
other gradient
impellers,
could
operation
the centrifugal
pump.Under
Velocity
gradient
flow rate conditions, the low speed velocity zone in Impeller 1 was the most obvious. Although
in Impellers
1–4 was
larger
and the flow in these impellers was disorderly. Under rated flow rate
6.2. Variation
of Relative
Velocity
differences of low speed zones of Impellers 2–5 were smaller, the zone of Impeller 5 was smaller than
conditions,Atthe
low
speed
velocity
zone
in Impeller
1 was
wassmall.
the most
obvious.
Although
differences
the inlet2–4.
of the
impeller,
the relative
velocity the
At the
outlet
ofof
the
impeller,
the
that of Impellers
Under
high flow
rate conditions,
low velocity
speed
zone
Impeller
5 was
of lowthe
speed
zones
of
Impellers
2–5
were
smaller,
the
zone
of
Impeller
5
was
smaller
than
relative
velocity
attained
the
maximum,
which
was
in
agreement
with
the
experimental
and
smallest. Velocity sudden change did not appear. The distribution of relative velocity wasthat of
Impellers
2–4.which
Under
high
flow
rate
conditions,
lowand
velocity
speed
zone
was
theoretical
results
[27]. Relative
velocity
in theΦthe
pressure
surface
much
than that
of the
uniform,
reflected
that blade
wrap angle
= 126°
bladewas
exit
angle
βsmaller
2 =of
24°Impeller
could
let 5the
suction
pressure.
Withchange
the
increase
of flow
rate,
the low
relative
speed
became
smaller,
as
smallest.
Velocity
sudden
did
appear.
The
distribution
of relative
velocity
was
uniform,
centrifugal
pump
operate
stably.
The not
hydraulic
performances
of Impeller
5 zone
were better
than
others.
in Figure
13. wrap angle Φ = 126◦ and blade exit angle β2 = 24◦ could let the centrifugal
whichshown
reflected
that blade
pump operate stably. The hydraulic performances of Impeller 5 were better than others.
0.6 Qd
0.6 Qd
0.8 Qd
0.8 Qd
1.2 Qd
1.5 Qd
(a) Impeller 1 (Φ = 122°, β2 = 26°)
1.0 Qd
1.2 Qd
1.0 Qd
1.5 Qd
(a) Impeller 1 (Φ = 122°, β2 = 26°)
0.6 Qd
0.8 Qd
1.0 Qd
1.2 Qd
1.5 Qd
0.6 Qd
0.8 Qd
1.0 Qd
1.2 Qd
1.5 Qd
(b) Impeller 2 (Φ = 126°, β2 = 26°)
Figure 13. Cont.
2018,
11, x FOR PEER REVIEW
EnergiesEnergies
2018, 11,
1444
0.6 Qd
0.8 Qd
11 of 2011 of 21
1.0 Qd
1.2 Qd
1.5 Qd
(c) Impeller 3 (Φ = 130°, β2 = 26°)
0.6 Qd
0.8 Qd
1.0 Qd
1.2 Qd
1.5 Qd
(d) Impeller 4 (Φ = 126°, β2 = 28°)
0.6 Qd
0.8 Qd
1.0 Qd
1.2 Qd
1.5 Qd
(e) Impeller 5 (Φ = 126°, β2 = 24°)
Figure 13. Variation of absolute velocity in different impellers.
Figure 13. Variation of absolute velocity in different impellers.
6.3. Variation of Streamlines
6.3. Variation of Streamlines
Under low flow rate conditions, streamlines in Impellers 1–4 were disorder and there were
manifest
vortices,
especially
for 0.6streamlines
Qd condition,
could1–4
cause
severe
energyand
lossthere
and were
Under low
flow rate
conditions,
in which
Impellers
were
disorder
secondary
flow.
For
Impeller
2,
the
vortices
were
the
most
obvious,
as
shown
in
Figure
14b.
The
manifest vortices, especially for 0.6 Qd condition, which could cause severe energy loss and secondary
centrifugal pumps under these two flow rate conditions operated unstably, which could induce
flow. For Impeller 2, the vortices were the most obvious, as shown in Figure 14b. The centrifugal
severe vibrations and noises [28] and the efficiency of the centrifugal pumps decreased. However,
pumps under these two flow rate conditions operated unstably, which could induce severe vibrations
the streamlines in Impeller 5 under these two conditions were smooth. The secondary flow could be
and noises
[28]
and the efficiency
the low
centrifugal
decreased.
However,
the high
streamlines
in
avoided
successfully.
Comparedofwith
flow ratepumps
conditions,
streamlines
in rated and
flow
Impeller
under these
two conditions
were smooth.
Theofsecondary
flow
could
avoided
successfully.
rate5 conditions
became
smooth. However,
streamlines
Impellers 1–4
were
morebe
disorder
than
that
Compared
with low
rate 1,
conditions,
streamlines
in rated
high flow
rate conditions
became
of Impeller
5. In flow
Impellers
2, and 4, the
low speed region
onand
the pressure
surface
was dramatic,
which
could let
the flow inofsuction
surface
faster.
lossthan
in this
could be
smooth.
However,
streamlines
Impellers
1–4was
were
moreEnergy
disorder
thatregion
of Impeller
5. caused
In Impellers
easily.
Overall,
the streamlines
in Impeller
5 weresurface
the smoothest,
as displayed
in Figure
1, 2, and
4, the
low speed
region on
the pressure
was dramatic,
which
could14e,
let which
the flow in
could result in lower energy loss. The flow separation and back flow could be controlled. The
suction surface was faster. Energy loss in this region could be caused easily. Overall, the streamlines in
centrifugal pump could operate stably.
Impeller 5 were the smoothest, as displayed in Figure 14e, which could result in lower energy loss.
The flow separation and back flow could be controlled. The centrifugal pump could operate stably.
Energies 2018, 11, 1444
12 of 21
Energies 2018, 11, x FOR PEER REVIEW
0.6 Qd
0.8 Qd
12 of 20
1.0 Qd
1.2 Qd
1.5 Qd
(a) Impeller 1 (Φ = 122°, β2 = 26°)
0.6 Qd
0.8 Qd
1.0 Qd
1.2 Qd
1.5 Qd
(b) Impeller 2 (Φ = 126°, β2 = 26°)
0.6 Qd
0.8 Qd
1.0 Qd
1.2 Qd
1.5 Qd
1.2 Qd
1.5 Qd
1.2 Qd
1.5 Qd
(c) Impeller 3 (Φ = 130°, β2 = 26°)
0.6 Qd
0.8 Qd
1.0 Qd
(d) Impeller 4 (Φ = 126°, β2 = 28°)
0.6 Qd
0.8 Qd
1.0 Qd
(e) Impeller 5 (Φ = 126°, β2 = 24°)
Figure 14. Variation of streamlines in different impeller.
Figure 14. Variation of streamlines in different impeller.
Energies
2018, 11,
11, x
FOR PEER REVIEW
Energies 2018,
1444
13
13 of
of 20
21
6.4. Variation of Turbulent Kinetic Energy
6.4. Variation of Turbulent Kinetic Energy
The distribution characteristics of turbulent kinetic energy in the middle span of the impeller
distribution
characteristics
of turbulent
energywhich
in the middle
span ofintheFigure
impeller
wereThe
sharply
different
under diverse
flow ratekinetic
conditions,
were shown
15.were
The
sharply different
under
diverse
flow rate
conditions,
were shown
in Figure
The distribution
distribution
scope
became
smaller
gradually
withwhich
the increase
of flow
rates.15.
Under
the 0.6 Qd
scope became
smaller gradually
the increase
flow was
rates.
Qd the
condition,
condition,
the distribution
range ofwith
turbulent
kinetic of
energy
the Under
largest the
and0.6
under
1.5 Qd
the distribution
range
ofthe
turbulent
was the largest and under the 1.5 Qd condition,
condition,
the scope
was
smallestkinetic
for all energy
the impellers.
the scope
was
the
smallest
for all the impellers.
Under
low
flow
rate conditions,
the distribution scope of turbulent kinetic energy in Impeller 2
Underthan
low flow
rate
conditions,
theVelocity
distribution
scope
turbulent
kinetic
energy
inflows
Impeller
was larger
that of
other
impellers.
vector
had of
obvious
change
when
water
from2
was
larger than
thatvolute.
of otherCentrifugal
impellers. Velocity
vector
had obvious
change
when water
flows
from
the
the impeller
to the
pump with
Impeller
2 could
not operate
stably.
Under
rated
impeller
to
the
volute.
Centrifugal
pump
with
Impeller
2
could
not
operate
stably.
Under
rated
flow
flow rate conditions, the turbulent kinetic energy distribution scopes of Impellers 1, 3, and 4 were
rate conditions,
turbulent
kinetic
scopes
Impellers
1, 3,rate
andconditions,
4 were similar
similar
and theythe
were
slightly
largerenergy
than distribution
that of Impeller
5. of
For
high flow
the
and they were
slightly
larger than
thatenergy
of Impeller
5. For identical
high flowfor
rate
the distribution
distribution
scope
of turbulent
kinetic
was almost
allconditions,
the impellers.
scopeBased
of turbulent
kineticanalysis
energy of
was
almost identical
for alland
the according
impellers. to Equation (7), turbulent
on the above
turbulent
kinetic energy
Based
on the
above analysis
of turbulent
kinetic
and according
to Equation
(7),
turbulent
intensity
l [29]
of Impeller
5 was less
intense than
thatenergy
of Impellers
1–4 overall.
Thus, the
energy
loss
intensity
l [29]
of Impeller
intense than
that
of Impellers
1–4the
overall.
Thus, the energy
loss in
in
Impeller
5 was
less than5 was
otherless
impellers,
which
could
guarantee
high transportation
capacity
Impeller
5 was less
than other impellers, which could guarantee the high transportation capacity of
of
the centrifugal
pump.
the centrifugal pump.
2
3
= 3 (vvininll)2
(10)
kk =
(10)
22
Here, vvin
is the
the inlet
inlet velocity.
velocity. ll is
is the
the turbulent
turbulent intensity.
intensity.
in is
Here,
(
0.6 Qd
0.8 Qd
)
1.0 Qd
1.2 Qd
1.5 Qd
(a) Impeller 1 (Φ = 122°, β2 = 26°)
0.6 Qd
0.8 Qd
1.0 Qd
1.2 Qd
1.5 Qd
(b) Impeller 2 (Φ = 126°, β2 = 26°)
0.6 Qd
0.8 Qd
1.0 Qd
(c) Impeller 3 (Φ = 130°, β2 = 26°)
Figure 15. Cont.
1.2 Qd
1.5 Qd
Energies 2018, 11, x FOR PEER REVIEW
Energies 2018, 11, 1444
Energies 2018, 11, x FOR PEER REVIEW
14 of 20
14 of 21
14 of 20
0.6 Qd
0.8 Qd
0.6 Qd
0.8 Qd (d) Impeller 41.0
(ΦQ=d126°, β2 = 28°)
1.0 Qd
1.2 Qd
1.5 Qd
1.2 Qd
1.5 Qd
(d) Impeller 4 (Φ = 126°, β2 = 28°)
0.6 Qd
0.8 Qd
0.6 Qd
0.8 Qd (e) Impeller 5 (1.0
d
Φ =Q126°,
β2 = 24°)
1.0 Qd
1.2 Qd
1.5 Qd
1.2 Qd
1.5 Qd
(e) Impeller 5 (Φ = 126°, β2 = 24°)
Figure 15. Variation of turbulent kinetic energy in different impellers.
Figure
of turbulent
turbulent kinetic
kinetic energy
energy in
in different
different impellers.
impellers.
Figure 15.
15. Variation
Variation of
58
90
56
58
88
90
54
56
86
88
52
54
84
86
50
52
82
84
48
50
46
48
44
46
42
44
40
42
Head of Scheme 1
Head of Scheme 2
Head of Scheme 1
Head of Scheme 3
Head of Scheme 2
Efficiency of Scheme 1
Head of Scheme 3
Efficiency of Scheme 2
Efficiency of Scheme 1
Efficiency of Scheme 3
Efficiency of Scheme 2
500
600
700 3 800
Efficiency
of Scheme
200
40
300
400
200
300
3
400 Flow
500rate Q/m
600 /h700
800
80
82
78
80
76
78
Efficiency
η/%η/%
Efficiency
Head
Head
H/mH/m
6.5. Variations of Head and Efficiency
6.5. Variations
of
Head and
Efficiency
With the of
increase
of Efficiency
flow rate, head decreased gradually and efficiency increased firstly then
6.5. Variations
Head and
decreased,
as
exhibited
in
16. Differences
of head
were relatively
slight. A
head with
Φ = 122°
With the increase of Figure
flow rate,
head decreased
gradually
and efficiency
increased
firstly
then
With the increase of flow rate, head decreased gradually and efficiency increased firstly then
was
higher as
than
that of in
Φ Figure
= 126°.16.
The
head of the
pump with
Φ=A
130°
was
theΦ
highest
decreased,
exhibited
Differences
of centrifugal
head were relatively
slight.
head
with
= 122°
decreased, as exhibited in Figure 16. Differences of head were relatively slight. A head with Φ = 122◦
one.
attained
designed
flow rate.pump
Efficiency
Φ = 130°
higher
was Efficiency
higher than
that ofthe
Φ =maximum
126°. Theunder
head of
the centrifugal
with with
Φ = 130°
was was
the highest
was higher than that of Φ = 126◦ . The head of the centrifugal pump with Φ = 130◦ was the highest one.
than
of Φ =attained
122° andthe
126°.
Compared
with
Schemesflow
1 and
2, Scheme
3 was
one.
one. that
Efficiency
maximum
under
designed
rate.
Efficiency
withthe
Φ =optimal
130° was
higher
Efficiency attained the maximum under designed flow rate. Efficiency with Φ = 130◦ was higher than
than that of Φ =◦ 122° and◦ 126°. Compared with Schemes 1 and 2, Scheme 3 was the optimal one.
that of Φ = 122 and 126 . Compared with Schemes 1 and 2, Scheme 3 was the optimal one.
74
76
72
74
90072
900
Flow rate Q/m3/h
Figure
Figure 16.
16. Hydraulic
Hydraulic performances
performances of
of the
the centrifugal
centrifugal pump
pump with
with different
different blade wrap angles.
Figure 16. Hydraulic performances of the centrifugal pump with different blade wrap angles.
Schemes
Schemes 2,
2, 4,
4, and
and 55 reflected
reflected the
the effects
effects of
of blade
blade exit
exit angles
angles on
on hydraulic
hydraulic performances
performances of
of the
the
centrifugal
pump,
as
displayed
in
Figure
17.
Head
decreased
constantly
and
efficiency
increased
Schemes
2, 4,asand
5 reflected
the effects
of blade
exit angles
on hydraulic
performances
the
centrifugal
pump,
displayed
in Figure
17. Head
decreased
constantly
and efficiency
increased of
firstly
firstly
then
decreased
with
the
increase
of
flow
rate.
The
efficiency
attained
the
maximum
under
the
centrifugal
pump,
as
displayed
in
Figure
17.
Head
decreased
constantly
and
efficiency
increased
then decreased with the increase of flow rate. The efficiency attained the maximum under the rated
rated
flow
Head
2 =◦ 24°
slightly
higher
than
that
2 = 28°.
Differences
of head
head
with
firstlyrate.
thenrate.
decreased
with
increase
of flow
rate. than
The
efficiency
the maximum
under
the
flow
Head
withwith
β2 =βthe
24
waswas
slightly
higher
that
of of
β2βattained
=
28◦ . Differences
of
with
βrated
2 = 26°and
28° Head
were with
sharp.
efficiency
wereofsmaller.
flow rate.
β2 The
= 24°distinctions
was slightlyof
higher
than that
β2 = 28°. Efficiency
Differencesofofcentrifugal
head with
β2 = 26°and 28° were sharp. The distinctions of efficiency were smaller. Efficiency of centrifugal
Energies 2018, 11, x FOR PEER REVIEW
15 of 20
pump with β2 = 24° was the highest. Compared with Schemes 2, 4, and 5, the centrifugal pump with
2018,
1444
15 of
of 20
21
βEnergies
2 = 24°2018,
had11,
the
bestPEER
hydraulic
Energies
11,
x FOR
REVIEWperformances.
15
pump with
β2 = 24° was the highest. Compared with Schemes 2, 4, and 5, the centrifugal pump with
β2 = 26◦ and 28◦ were sharp. The distinctions of efficiency were smaller. Efficiency of centrifugal pump
β2 = 24° had the best hydraulic performances.
with β2 = 24◦ was the highest.60Compared with Schemes 2, 4, and 5, the centrifugal
pump with β2 = 24◦
90
58
had the best hydraulic performances.
88
54
60
52
58
86
50
56
48
54
88
82
90
84
84
78
Head of Scheme 5
42
48
40
46
44200
86
80
Head of Scheme 2
Head of Scheme 4
46
52
44
50
Efficiency of Scheme 2
82
76
Head of Scheme
2 4
Efficiency
of Scheme
80
74
Head of Scheme
4 5
Efficiency
of Scheme
300
400
3
Efficiency of Scheme
2
78
72
900
76
Efficiency of Scheme 4
74
Head of Scheme
500
600 5 700
800
Flow rate Q/m /h
42
40
Efficiency
η/%
Efficiency η
/%
Head H/m Head H/m
56
Efficiency of Scheme 5
72
Figure 17. Hydraulic performances
of
centrifugal
pump
200
300
400 the500
600
700
800with
900different blade exit
3
Flow rate Q/m /h
angles.
Figure
performances
of130°
the centrifugal
pump
with
different
blade
exit angles.
Figure
17. 17.
Hydraulic
performances
the
centrifugal
pump
with
different
blade
exit blade exit
In
Scheme
3, Hydraulic
blade wrap
angle Φ =of
was the optimal
one.
The
corresponding
angleangles.
β2 = 26°. In Scheme 5, blade exit angle β2 = 24° was the best one. The corresponding blade wrap
◦ was 5
angleInΦScheme
= 126°.3,Head
efficiency
Scheme
were
higher
of Scheme blade
3, as shown
in
bladeand
wrap
angle Φ of
= 130
the
optimal
one.than
Thethat
corresponding
exit angle
◦
◦
In
Scheme
3,
blade
wrap
angle
Φ
=
130°
was
the
optimal
one.
The
corresponding
blade
exit
Figure
Scheme
5 was
hydraulic
the wrap
centrifugal
β2 = 26 18.
. InSo,
Scheme
5, blade
exitselected
angle β2to= improve
24 was the best
one. Theperformances
correspondingofblade
angle
angle
β2◦=. Head
26°. Inand
Scheme
5, blade
exit angle
β2 = 24°
wasthan
the best
The corresponding
blade
wrap
pump.
Φ = 126
efficiency
of Scheme
5 were
higher
thatone.
of Scheme
3, as shown in
Figure
18.
angle
Φ = 126°.
andtoefficiency
5 were
higher than
thatcentrifugal
of Schemepump.
3, as shown in
So, Scheme
5 wasHead
selected
improve of
theScheme
hydraulic
performances
of the
Figure 18. So, Scheme 5 was selected to improve the hydraulic performances of the centrifugal
60
pump.
90
58
86
Head H/m Head H/m
54
60
90
84
52
58
88
82
50
56
86
80
48
54
Head of Scheme 3
Head of Scheme 5
Efficiency of Scheme 3
Efficiency of Scheme 5
46
52
44
50
42
48
46200
44
42
300
Head of Scheme 3
500
600
700
800
Head of Scheme 5
3
Flow Efficiency
rate Q/mof
/hScheme 3
Efficiency of Scheme 5
400
84
78
82
76
80
74
90078
η/%
Efficiency
/%
Efficiency η
88
56
76
74
Figure
Hydraulic
of Schemes
3 and 5.
20018. Hydraulic
300
400 performances
500
600
700
800
900
Flow rate Q/m3/h
7. Experimental
Experimental Analysis
Figure 18. Hydraulic performances of Schemes 3 and 5.
Via numerical
numericalsimulation
simulation
in Part
6, Scheme
5 was determined
to one.
be the
one. The
in Part
6, Scheme
5 was determined
to be the best
Thebest
corresponding
corresponding
impeller was
machined.
Then, theexperiments
performancewere
experiments
done performance
in the closed
impeller was machined.
Then,
the performance
done in were
the closed
7. Experimental Analysis
performance
experiment
rigKaiquan
of Shanghai
Kaiquan
Pump
Group
to verify
that head of
and
of
experiment rig
of Shanghai
Pump
Group to
verify
that head
and efficiency
theefficiency
centrifugal
Via
numerical
simulation
in obvious
Part5 showing
6, improvement.
Scheme
5 wasimprovement.
determined to be the best one. The
the
centrifugal
with
the Impeller
obvious
pump
with
the pump
Impeller
5 showing
corresponding impeller was machined. Then, the performance experiments were done in the closed
Experiment Setup
Setup
performance
experiment rig of Shanghai Kaiquan Pump Group to verify that head and efficiency of
Experiment
the centrifugal
pump
with the Impeller
5 showing
obvious
improvement.
impeller
machining
processwas
was
displayed
Figure
outlet
of impeller,
the impeller,
The impeller
machining
process
displayed
ininFigure
19.19.
At At
the the
outlet
of the
the
the
allowance
was
5
mm,
as
shown
in
region
A.
Allowance
of
the
impeller
front
shroud
and
back
allowance was 5 mm, as shown in region A. Allowance of the impeller front shroud and back shroud
Experiment Setup
shroud
was as
3 mm,
as exhibited
in region
B. At
the of
inlet
the impeller,
the allowance
3 mm
was
3 mm,
exhibited
in region
B. At the
inlet
theofimpeller,
the allowance
waswas
3 mm
too,too,
as
as displayed
in region
Allowance
ofwas
the
hub
was
3 in
mm,
as
shown
region
The impeller
machining
process
displayed
Figure
19.inAtin
the
outlet
displayed
in region
C. C.
Allowance
of the
hub
was
3 mm,
as
shown
region
D.D. of the impeller, the
allowance was 5 mm, as shown in region A. Allowance of the impeller front shroud and back shroud
was 3 mm, as exhibited in region B. At the inlet of the impeller, the allowance was 3 mm too, as
displayed in region C. Allowance of the hub was 3 mm, as shown in region D.
Energies 2018, 11, x FOR PEER REVIEW
16 of 20
A
Energies 2018, 11, 1444
16 of 21
Energies 2018, 11, x FOR PEER REVIEW
16 of 20
B
A
B
C
C
D
D
Figure Figure
19. The
machining
process
19. The machining
processofofthe
the impeller.
impeller.
Figure 19. The machining process of the impeller.
Tothe
measure
the optimized
of impeller
the impeller
Scheme 5, 3D
impeller,
givengiven
in
To measure
optimized
designdesign
of the
ofofScheme
3Dwax
waxpattern
pattern
impeller,
in
To measure
the
optimized
design
of the
impeller
of prototyping
Scheme 5, 3Dmachine,
wax pattern
impeller,
given 21.
Figure
20,
was
machined
firstly
in
the
HRPS-V
rapid
as
shown
in
Figure
Figure 20, was machined firstly in the HRPS-V rapid prototyping machine, as shown in Figure 21.
in Figure
20, was
machined
firstly in (LOM)
the HRPS-V
prototyping machine,
as shown
incoming
Figure 21.
Laminated
object
manufacturing
in thisrapid
machine—which
is based on
the data
from
Laminated
object
manufacturing
(LOM)
in
this
machine—which
is
based
on
the
data
coming from
Laminated
object
manufacturing
(LOM)
in hot
thispressing
machine—which
is based
on thetodata
coming
CAD laying
model,
CO2 laser beam,
and
device—was
employed
machine
the from
3D wax
CAD laying
model,
CO2 laser
beam,
and
hot
device—was
employed
to machine
the 3D wax
CAD
layingimpeller.
model,
CO2 laser
beam,
and
hotpressing
pressing device—was
employed
to machine
the 3D wax
pattern
pattern impeller.
pattern impeller.
Figure 20. 3D wax pattern.
Figure20.
20.3D
3D wax
Figure
waxpattern.
pattern.
Figure 21. HRPS-V rapid prototyping machine.
Then, the casted impeller of Scheme 5 was machined, which was displayed in Figure 22. The
material was 2Cr13. To guarantee that the passages of the impeller were smooth and clean, silt
particles and cast jointFigure
flash in21.
theHRPS-V
passagesrapid
were prototyping
cleaned carefully.
machine.
Figure 21. HRPS-V rapid prototyping machine.
Then, the
casted
impeller
of Scheme
5 was
machined,
displayedin in
Figure
Then,
the casted
impeller
of Scheme
5 was
machined,which
which was
was displayed
Figure
22. 22. The
To guarantee
thatpassages
the passages
of the
impeller were
were smooth
andand
clean,
materialThe
wasmaterial
2Cr13.was
To2Cr13.
guarantee
that the
of the
impeller
smooth
clean, silt
silt particles and cast joint flash in the passages were cleaned carefully.
particles and cast joint flash in the passages were cleaned carefully.
Figure 22. The casted impeller.
Figure 21. HRPS-V rapid prototyping machine.
Then, the casted impeller of Scheme 5 was machined, which was displayed in Figure 22. The
material
was 2Cr13. To guarantee that the passages of the impeller were smooth and 17
clean,
silt
Energies 2018, 11, 1444
of 21
particles and cast joint flash in the passages were cleaned carefully.
Energies 2018, 11, x FOR PEER REVIEW
Energies 2018, 11, x FOR PEER REVIEW
Figure
impeller.
Figure22.
22. The
The casted
casted impeller.
17 of 20
17 of 20
The
atat
thethe
closed
experiment
rigrig
of
The performance
performance experiments
experimentsof
ofthe
thecentrifugal
centrifugalpump
pumpwere
weredone
done
closed
experiment
The
performance
experiments
of
the
centrifugal
pump
were
done
at
the
closed
experiment
rig
Shanghai
Kaiquan
Pump
Group.
The experiment
rig, given
Figurein23,Figure
includes
model centrifugal
of Shanghai
Kaiquan
Pump
Group.
The experiment
rig,ingiven
23,the
includes
the model
of
Shanghai
Kaiquan
Pump
Group.
The
experiment
rig,
given
in
Figure
23,
includes
thetype
model
pump,
suction
pipes,
exit
pipes,
pressure
gauges,
valves,
and
flow
meters.
The
type
of
pressure
sensor
centrifugal pump, suction pipes, exit pipes, pressure gauges, valves, and flow meters. The
of
centrifugal
pump,
suction
pipes,
exit
pipes,
pressure
gauges,
valves,
and
flow
meters.
The
type
of
is
XU12087105
(1.0,
Shanghai
Automation
Instrumentation
Co.
Ltd.,
Shanghai,
China).
The
type
of
pressure sensor is XU12087105 (1.0, Shanghai Automation Instrumentation CO. LTD, Shanghai,
pressure
sensor
is
XU12087105
(1.0,
Shanghai
Automation
Instrumentation
CO.
LTD,
Shanghai,
flow
meter
DN300
(1.0,meter
Tianjin
Flow Meter
Co. Ltd.,
Tianjin,
The
type ofChina).
valve is
ZA2.T.
China).
Theistype
of flow
is DN300
(1.0, Tianjin
Flow
MeterChina).
CO. LTD,
Tianjin,
The
type
China).
The
type
of
flow
meter
is
DN300
(1.0,
Tianjin
Flow
Meter
CO.
LTD,
Tianjin,
China).
The
All
testing
precisions
are
national
grade
1
(GB3216-2005
and
ISO
9906-1999).
of valve is ZA2.T. All testing precisions are national grade 1 (GB3216-2005 and ISO 9906-1999). type
of valve is ZA2.T. All testing precisions are national grade 1 (GB3216-2005 and ISO 9906-1999).
Figure 23.
23. Performance
Performance experiment
experiment rig.
rig.
Figure
Figure 23. Performance experiment rig.
Figure 24 is the typical components of the closed performance experiment rig. It includes 16
Figure
24
Figure
24 is
is the
the typical
typical components
components of
of the
the closed
closedperformance
performance experiment
experiment rig.
rig. It
It includes
includes 16
16
different
parts.
different
different parts.
parts.
Figure 24. Components of the closed performance experiment rig. 1–electric motor; 2–torque and
Figuresensor;
24. Components
of the closed
performance
experiment
rig. 1–electric
motor; 2–torque
and
speed
3–centrifugal
4–sluice
valve;
5–inlet
pressure
sensor;
6–turbine
flow
Figure
24. Components
of thepump;
closed performance
experiment
rig. 1–electric
motor;
2–torque
andmeter;
speed
speed sensor;
3–centrifugal
pump; 4–sluice
valve; 5–inlet
pressure
sensor;
6–turbineflow
flowmeters;
meter;
7–outlet
pressure
sensor;
flow 5–inlet
meter;
9–expansion
10–turbine
sensor;
3–centrifugal
pump; 8–turbine
4–sluice valve;
pressure
sensor;joint;
6–turbine
flow meter; 7–outlet
7–outlet
pressure
sensor;
8–turbine
flow
meter;
9–expansion
joint;
10–turbine
flow
meters;
11–regulating
12–turbine
flow 9–expansion
meters; 13–cavitation
tank; 14–separation
tank of vaporvalve;
and
pressure
sensor;valve;
8–turbine
flow meter;
joint; 10–turbine
flow meters; 11–regulating
11–regulating
valve; 16–
12–turbine
flow meters;
13–cavitation
tank; 14–separation tank of vapor and
water;
15–ball
valve;
electric motor;
17–vacuum
pump. tank
12–turbine
flow
meters; 13–cavitation
tank;
14–separation
of vapor and water; 15–ball valve;
water; 15–ball valve; 16– electric motor; 17–vacuum pump.
16–electric motor; 17–vacuum pump.
Via the inlet pressure Sensor 5 and the outlet pressure Sensor 7, M1 and M2 were determined.
Via thetoinlet
pressure
Sensor
5 and
outlet
pressure
7, M1pressure
and M2 were
According
Equations
(11)
and (12),
thethe
inlet
pressure
andSensor
the outlet
of thedetermined.
centrifugal
According
to
Equations
(11)
and
(12),
the
inlet
pressure
and
the
outlet
pressure
of the centrifugal
pump could be got.
pump
could
got.
The
inletbe
pressure
is calculated by
The inlet pressure is calculated by
p1
p = 102 M + h
ρ g1 = 102 M11 + h11
ρg
(11)
(11)
Energies 2018, 11, 1444
18 of 21
Via the inlet pressure Sensor 5 and the outlet pressure Sensor 7, M1 and M2 were determined.
According to Equations (11) and (12), the inlet pressure and the outlet pressure of the centrifugal pump
could be got.
The inlet pressure is calculated by
p1
= 102M1 + h1
ρg
(11)
p2
= 102M2 − h3
ρg
(12)
The outlet pressure is determined by
where h1 is the vertical height between the center of inlet pressure sensor with axial lead of the
centrifugal pump. h3 is the vertical height between the center of the outlet pressure sensor with the
outlet pressure port.
The inlet flow rate (Q1 ) and outlet flow rate (Q2 ) of the centrifugal pump could be measured by
turbine flow meter 6 and 8, respectively.
Thus, the inlet velocity of the centrifugal pump v1 could be calculated by
v1 =
Q1
A1
(13)
The outlet velocity of the centrifugal pump v2 could be got by
v2 =
Q2
A2
(14)
Here, A1 is the inlet cross-section area. A2 is the outlet cross-section area.
Head (H) could be calculated by Equation (15)
H=
p2
p
− 1
ρg ρg
+
v2
v22
− 1
2g 2g
!
+ ( Z2 − Z1 )
(15)
where Z2 and Z1 are the static head.
In the performance experiment rig,
Z1 = 0
(16)
Z2 = h2 + h3
(17)
For Z2 , it could be obtained by
Here, h2 is the vertical height between the center of outlet pressure sensor with axial lead of the
centrifugal pump.
In the performance experiment rig,
h2 = h1
(18)
The Equation (15) could be modified. The new form was shown in Equation (20).
H = 102( M2 − M1 ) +
v2
v22
− 1
2g 2g
!
(19)
Efficiency (η) could be calculated by Equation (16)
η=
ρgQH
× 100%
1000P
(20)
Energies 2018, 11, 1444
19 of 21
Here, P is the inlet power, which could be measured by torque and speed sensor 2.
Hydraulic performance curves of the improved centrifugal pump and the original centrifugal
pump were shown in Figure 25. Experimental results indicated that head and efficiency of the
improved centrifugal pump were higher than that of the original centrifugal pump. Under low flow
rate condition (0.8 Qd ), the head increased by 3.76 m and the efficiency increased by 3.84%. With
rated flow rate condition (1.0 Qd ), the head increased by 2.74 m and the efficiency increased by 5.77%,
Energies
2018, 11,
x FOR
PEER
REVIEW
19 of
20
separately.
For
high
flow
rate condition (1.2 Qd ), the head and efficiency increased by 2.67 m and
5.0%,
respectively. The experimental results indicated that the optimized design is successful.
100
60
Head H/m
50
60
45
40
40
Head of original centrifugal pump
Efficiency η/%
80
55
20
Head of improved centrifugal pump
35
Efficiency of original centrifugal pump
Efficiency of improved centrifugal pump
30
0
200
400
600
800
0
1000
3
Flow rate Q/m /h
Figure25.
25.Hydraulic
Hydraulicperformance
performanceofofimproved
improvedand
andoriginal
originalcentrifugal
centrifugalpump.
pump.
Figure
Conclusions
8.8.Conclusions
thispaper,
paper,effects
effectsofofblade
bladeexit
exitangle
angleand
andblade
bladewrap
wrapangle
angleon
onthe
theoptimized
optimizeddesign
designofofthe
the
InInthis
impellerwere
werecomprehensively
comprehensivelyinvestigated.
investigated.Flows
Flowsininthe
thecentrifugal
centrifugalpump
pumpwith
withfive
fivedifferent
different
impeller
impellersunder
underlow
lowflow
flowrate,
rate,rated
ratedflow
flowrate,
rate,and
andhigh
highflow
flowrate
ratewere
werenumerically
numericallysimulated.
simulated.
impellers
Variations of static
velocity,
streamlines,
and turbulent
kinetickinetic
energy were
analyzed.
Variations
staticpressure,
pressure,relative
relative
velocity,
streamlines,
and turbulent
energy
were
Head andHead
efficiency
of the centrifugal
pump of different
schemes
were
compared.
experimental
analyzed.
and efficiency
of the centrifugal
pump of
different
schemes
wereThe
compared.
The
head
and
efficiency
of
the
centrifugal
pump
with
the
best
impeller
were
compared
with
that
of
the
experimental head and efficiency of the centrifugal pump with the best impeller were compared
original
The main
conclusions
areconclusions
as follows: are as follows:
with
that impeller.
of the original
impeller.
The main
◦ and blade exit angle 24◦ was the best one.
(1) The
Theimpeller
impellerwith
withblade
bladewrap
wrapangle
angle126°
126and
(1)
blade exit angle 24° was the best one.
(2) For
Forthe
thebest
bestimpeller,
impeller,static
staticpressure
pressureand
andrelative
relativevelocity
velocitywas
wasthe
themost
mostuniform
uniformdistribution.
distribution.
(2)
Streamlines
were
the
smoothest
and
vortices
did
not
exist.
Compared
with
other
impellers,
Streamlines were the smoothest and vortices did not exist. Compared with other impellers,
the
the
distribution
scope
of
turbulent
kinetic
energy
in
the
best
impeller
under
all
flow
rate
conditions
distribution scope of turbulent kinetic energy in the best impeller under all flow rate
was the smallest.
conditions
was the smallest.
(3)
For
the
centrifugal
pumpwith
withoptimized
optimizedimpeller,
impeller,head
headand
andefficiency
efficiencywere
werehigher
higherthan
thanthat
thatofof
(3) For the centrifugal pump
theoriginal
originalpump.
pump.With
Withlow
lowflow
flowrate
rate(0.8
(0.8QQ
thehead
headand
andefficiency
efficiencyincreased
increasedby
by3.76
3.76mmand
and
the
d),
the
d ),
3.84%.With
Withrated
ratedflow
flowrate,
rate,the
thehead
headand
andefficiency
efficiencyincreased
increasedby
by2.74
2.74mmand
and5.77%.
5.77%.With
Withhigh
high
3.84%.
flowrate
rate(1.2
(1.2QQ
the
head
and
efficiency
increasedbyby2.67
2.67mmand
and5.0%.
5.0%.
flow
d),d ),
the
head
and
efficiency
increased
Author
presented the
theoptimal
optimalscheme
schemeand
anddesigned
designed
experiments.
X.H.
AuthorContributions:
Contributions:X.H.
X.H.and
and Y.K.
Y.K. presented
thethe
experiments.
X.H.
andand
D.L.
made
the numerical
simulation
and performed
the experiment.
W.Z. analyzed
the data.
paper.
D.L.
made
the numerical
simulation
and performed
the experiment.
W.Z. analyzed
theX.H.
data.wrote
X.H.the
wrote
the
paper.
Acknowledgments: This research is financially supported by the National Key Basic Research Program of China
(no. 2014CB239203), the National Natural Science Foundation of China (no. 51474158), and the Hubei Provincial
Acknowledgments: This research is financially supported by the National Key Basic Research Program of
Natural Science Foundation of China (no. 2016CFA088). We deeply acknowledge the help of Hubei Key Laboratory
China
(no. 2014CB239203),
theTechnology,
National Natural
Foundation
of China
(no. 51474158),
andUniversity
the Hubeiof
of Waterjet
Theory and New
SchoolScience
of Energy
and Power
Engineering
of Lanzhou
Provincial
Natural
Science Foundation
of China (no. 2016CFA088). We deeply acknowledge the help of Hubei
Technology,
and Shanghai
Kaiquan Group.
Key Laboratory of Waterjet Theory and New Technology, School of Energy and Power Engineering of Lanzhou
Conflicts of Interest: The authors declare no conflict of interest.
University of Technology, and Shanghai Kaiquan Group.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
Yedidiah, S. Centrifugal Pump User’s Guidebook: Problems and Solutions; Springer Group: Berlin, Germany,
Energies 2018, 11, 1444
20 of 21
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
Yedidiah, S. Centrifugal Pump User’s Guidebook: Problems and Solutions; Springer Group: Berlin, Germany, 1996.
Gülich, J.F. Centrifugal Pumps; Springer Group: Berlin, Germany, 2008.
Karassik, I.J. Centrifugal Pump Clinic; Taylor Francis Inc.: Oxford, UK, 1989.
Tuzson, J. Centrifugal Pump Design; Wiley-Interscience: Washington, DC, USA, 2000.
Grist, E. Cavitation and the Centrifugal Pump: A Guide for Pump Users; Taylor Francis Inc.: Oxford, UK, 1998.
Lobanoff, V.S.; Ross, R.R. Centrifugal Pump: Design and Application; Gulf Professional Publishing: Houston,
TX, USA, 1992.
Girdhar, P.; Moniz, O. Practical Centrifugal Pumps. Design, Operation, Maintenance; Newnes: Amsterdam,
The Netherlands, 2005.
Wu, Z.H. Three-dimensional turbomachine flow equations expressed with respect to non-orthogonal
curvilinear coordinates and non-orthogonal velocity components and methods of solution. J. Mech. Eng.
1979, 15, 1–23.
Zhang, Z.H. Streamline similarity method for flow distribution and shock losses at the impeller inlet of the
centrifugal pump. J. Hydrodyn. 2018, 30, 140–152. [CrossRef]
Pei, J.; Wang, W.J.; Yuan, S.Q.; Zhang, J.F. Optimization on the impeller of a low-specific-speed centrifugal
pump for hydraulic performance improvement. Chin. J. Mech. Eng. 2017, 29, 992–1002. [CrossRef]
Tan, L.; Zhu, B.S.; Cao, S.L.; Bing, H.; Wang, Y.M. Influence of blade wrap angel on centrifugal pump
performance by numerical and experimental study. Chin. J. Mech. Eng. 2014, 27, 171–177. [CrossRef]
Kim, J.H.; Lee, H.C.; Kim, J.H.; Kim, S.; Yoon, J.Y.; Choi, Y.S. Design techniques to improve the performance
of a centrifugal pump using CFD. J. Mech. Sci. Technol. 2015, 29, 215–225. [CrossRef]
Stepanoff, A.J. Centrifugal and Axial Pump: Theory, Design and Application; John Wiley Sons Inc.: Hoboken, NJ,
USA, 1986.
Yang, A.L.; Lang, D.P.; Li, G.P.; Chen, E.Y.; Dai, R. Numerical research about influence of blade outlet angel
on flow-induced noise and vibration for centrifugal pump. Adv. Mech. Eng. 2015, 6, 1–11.
Heo, M.W.; Kim, J.H.; Seo, T.W.; Kim, K.Y. Aerodynamic and aeroacoustic optimization for design of a
forward-curved blades centrifugal fan. Proc. Inst. Mech. Eng. Part A J. Power Energy 2017, 230, 154–174.
[CrossRef]
Guan, X.F. Modern Pumps Theory and Design; China Astronautic Publishing House: Beijing, China, 2011.
(In Chinese)
Bai, Y.X.; Kong, F.Y.; Yang, S.S.; Chen, K.; Dai, T. Effect of blade wrap angel in hydraulic turbine with
forward-curved blades. Int. J. Hydrogen Energy 2017, 42, 18709–18717. [CrossRef]
Wang, W.J.; Pei, J.; Yuan, S.Q.; Zhang, J.F.; Yuan, J.P.; Xu, C.Z. Application of different surrogate models on
the optimization of centrifugal pump. J. Mech. Sci. Technol. 2016, 30, 567–574. [CrossRef]
Zhou, L.; Shi, W.D.; Wu, S.Q. Performance optimization in a centrifugal pump impeller by orthogonal
experiment and numerical simulation. Adv. Mech. Eng. 2013, 6, 1–11. [CrossRef]
Nelik, L. Centrifugal and Rotary Pumps: Fundamentals with Applications; CRC Press: London, UK, 1999.
Li, W.G.; Su, F.Z.; Ye, Z.M.; Xia, D.L. Experiment on effect of blade pattern on performance of centrifugal oil
pumps. Chin. J. Appl. Mech. 2002, 19, 31–34. [CrossRef]
Lohner, R. Applied Computational Fluid Dynamics Techniques: An Introduction Based on Finite Element Methods;
John Wiley & Sons: Hoboken, NJ, USA, 2008.
Yakhot, V.; Orzag, S.A. Renormalization group analysis of turbulence: Basic theory. J. Sci. Comput. 1986,
1, 3–51. [CrossRef]
Zhou, L.; Shi, W.D.; Li, W.; Agarwal, R. Numerical and experimental study of axial force and hydraulic
performance in a deep-well centrifugal pump with different impeller rear shroud radius. J. Fluid Eng. 2013,
135, 749–760. [CrossRef]
Posa, A.; Lippolis, A. A LES investigation of off-design performance of a centrifugal pump with
variable-geometry diffuser. Int. J. Heat Fluid Flow 2018, 70, 299–314. [CrossRef]
Chen, H.X.; He, J.W.; Liu, C. Design and experiment of the centrifugal pump impellers with twisted inlet
vice blades. J. Hydrodyn. 2017, 29, 1085–1088. [CrossRef]
Yang, S.L.; Kong, F.Y.; Chen, H.; Su, X.H. Effects of blade wrap angel influencing a pump as turbine.
J. Fluid Eng. 2012, 134, 1–8. [CrossRef]
Energies 2018, 11, 1444
28.
29.
21 of 21
Cheah, K.W.; Lee, T.S.; Winoto, S.H.; Zhao, Z.M. Numerical flow simulation in a centrifugal pump at design
and off-design conditions. Int. J. Rotating Mach. 2007, 2, 1–9. [CrossRef]
Ferziger, J.H.; Peric, M. Computational Methods for Fluid Dynamics; Springer Group: Berlin, Germany, 2002.
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).